Finite Group Databasebeta

← C2×#10599436 #12129209

Subgroups — C2×#10599436 #12129209

Order 1280.

998 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65217C211yesmaximal, characteristic
2C2×#65224C211yesmaximal, characteristic
3C2×C5×#336C211yesmaximal, characteristic
4C2×#64771C212yesmaximal
5C2×#64771C212yesmaximal
6#10599436C218yesmaximal, direct product factor
7C23×C5×C8C2212yes—
8C22×C42×C5C2211yescharacteristic
9C22×C4⋊Dic5—21no—
10C22×C4⋊Dic5—21no—
11C22×C4⋊Dic5C2212yes—
12C22×C4⋊Dic5C2211yescharacteristic
13C22×C4⋊Dic5C2211yescharacteristic
14C22×#683—21no—
15C2×#3963—21no—
16#65224—22no—
17#65224C2214yes—
18#65217—22no—
19#65217C2214yes—
20C5×#336C2214yes—
21#64771C2218yes—
22#64771C2218yes—
23C2×#2100—51nomaximal, Sylow
24C23×C4×C5D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C23×Dic5—21no—
28C23×Dic5—21no—
29C23×Dic5—22no—
30C22×C5×C8—24no—
31C22×C5×C8—24no—
32C22×C5×C8—24no—
33C22×C5×C8C2314yes—
34C2×C42×C5—24no—
35C2×C42×C5D412yes—
36C2×C42×C5C2312yes—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—22no—
39C2×C4⋊Dic5—28no—
40C2×C4⋊Dic5—24no—
41C2×C4⋊Dic5—24no—
42C2×C4⋊Dic5—24no—
43C2×C4⋊Dic5—21no—
44C2×C4⋊Dic5—22no—
45C2×C4⋊Dic5—44no—
46C2×C4⋊Dic5—44no—
47C2×C4⋊Dic5Q814yes—
48C2×C4⋊Dic5C2312yes—
49C2×C4⋊Dic5C2314yes—
50C2×C4⋊Dic5C2312yes—
51C2×#683—24no—
52C2×#683—44no—
53#3963—24no—
54C2×#389—51no—
55C2×#384—51no—
56#2100—58no—
57C2×#340—52no—
58C2×#340—52no—
59C2×#336D511yescharacteristic
60C24×C5C2×D411yescharacteristic
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5—22no—
64C22×C4×C5—22no—
65C22×C4×C5SD1614yes—
66C22×C4×C5Q1614yes—
67C22×C4×C5C2×D412yes—
68C22×C4×C5C2×D412yes—
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5C2×Q812yes—
71C22×C4×C5#4114yes—
72C22×C4×C5#4112yes—
73C22×C4×C5#4114yes—
74C22×C4×C5C2411yescharacteristic
75C22×Dic5—24no—
76C22×Dic5—22no—
77C22×Dic5—22no—
78C22×Dic5—24no—
79C22×Dic5—42no—
80C22×Dic5—42no—
81C22×Dic5—42no—
82C22×Dic5—44no—
83C22×Dic5—42no—
84C22×Dic5—42no—
85C22×Dic5—44no—
86C22×Dic5—44no—
87C2×C5×C8—24no—
88C2×C5×C8—24no—
89C2×C5×C8—24no—
90C2×C5×C8—48no—
91C42×C5—24no—
92C42×C5—24no—
93C4⋊Dic5—24no—
94C4⋊Dic5—22no—
95C4⋊Dic5—28no—
96C4⋊Dic5—24no—
97C4⋊Dic5—48no—
98C4⋊Dic5—48no—
99C4⋊Dic5—42no—
100C4⋊Dic5—44no—
101C4⋊Dic5C2×Q814yes—
102#683—48no—
103C23×C8C2×D512yes—
104C22×C4⋊C4—51no—
105C22×C4⋊C4—52no—
106C22×C4⋊C4—51no—
107C22×C4⋊C4—101no—
108C22×C4⋊C4—101no—
109C22×C4⋊C4—101no—
110C22×C42C2×D511yescharacteristic
111#389—54no—
112#389—102no—
113#384—54no—
114#384—102no—
115C2×#95—101no—
116#340—58no—
117#340—58no—
118#336C2×D514yes—
119C23×C5C22⋊Q812yes—
120C23×C5#12312yes—
121C23×C5#12412yes—
122C23×C5C2×SD1612yes—
123C23×C5C2×Q1612yes—
124C23×C5AGL(1,ℤ/8)12yes—
125C23×C5AGL(1,ℤ/8)12yes—
126C23×C5C22×D411yescharacteristic
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—22no—
131C2×C4×C5—28no—
132C2×C4×C5—28no—
133C2×C4×C5C22⋊Q812yes—
134C2×C4×C5#12312yes—
135C2×C4×C5#12412yes—
136C2×C4×C5#12518yes—
137C2×C4×C5#12618yes—
138C2×C4×C5C2×SD1614yes—
139C2×C4×C5C2×Q1614yes—
140C2×C4×C5C22×Q811yescharacteristic
141C2×C4×C5C2×#4112yes—
142C2×C4×C5C2×#4112yes—
143C2×C4×C5C2×#4111yescharacteristic
144C2×Dic5—24no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—48no—
148C2×Dic5—42no—
149C2×Dic5—44no—
150C2×Dic5—42no—
151C2×Dic5—44no—
152C2×Dic5—44no—
153C2×Dic5—42no—
154C2×Dic5—84no—
155C2×Dic5—88no—
156C5×C8—44no—
157C23×C4—101no—
158C23×C4—102no—
159C23×C4—101no—
160C23×C4D2011yescharacteristic
161C23×C4D2011yescharacteristic
162C23×C4C22×D511yescharacteristic
163C22×C8—24no—
164C22×C8—24no—
165C22×C8—24no—
166C22×C8C22×D514yes—
167C2×C4⋊C4—54no—
168C2×C4⋊C4—52no—
169C2×C4⋊C4—54no—
170C2×C4⋊C4—52no—
171C2×C4⋊C4—101no—
172C2×C4⋊C4—102no—
173C2×C4⋊C4—108no—
174C2×C4⋊C4—104no—
175C2×C4⋊C4—102no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4—104no—
178C2×C4⋊C4—104no—
179C2×C4⋊C4—104no—
180C2×C4⋊C4—204no—
181C2×C4⋊C4—204no—
182C2×C4⋊C4—204no—
183C2×C42—24no—
184C2×C42D2012yes—
185C2×C42C22×D512yes—
186#95—104no—
187C22×C5#40014yes—
188C22×C5#47614yes—
189C22×C5#47714yes—
190C22×C5#48114yes—
191C22×C5#48414yes—
192C22×C5#48714yes—
193C22×C5#49014yes—
194C22×C5C2×C22⋊Q811yescharacteristic
195C22×C5C2×#12311yescharacteristic
196C22×C5C2×#12411yescharacteristic
197C22×C5C22×SD1611yescharacteristic
198C22×C5C22×Q1611yescharacteristic
199C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
200C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
201C4×C5—24no—
202C4×C5—24no—
203C4×C5#40014yes—
204C4×C5C2×#12512yes—
205C4×C5C2×#12612yes—
206Dic5—44no—
207Dic5—82no—
208Dic5—84no—
209C24C2×D2011yescharacteristic
210C22×C4—22no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—102no—
215C22×C4—104no—
216C22×C4—102no—
217C22×C4—104no—
218C22×C4—202no—
219C22×C4—202no—
220C22×C4—204no—
221C22×C4—202no—
222C22×C4—202no—
223C22×C4—204no—
224C22×C4—204no—
225C22×C4—202no—
226C22×C4#67714yes—
227C22×C4Dic2014yes—
228C22×C4C2×D2012yes—
229C22×C4C2×D2012yes—
230C22×C4C2×D2011yescharacteristic
231C22×C4#70914yes—
232C22×C4#71112yes—
233C22×C4#71114yes—
234C22×C4Q8×D512yes—
235C22×C4C23×D511yescharacteristic
236C2×C8—24no—
237C2×C8—24no—
238C2×C8—24no—
239C2×C8—48no—
240C4⋊C4—54no—
241C4⋊C4—102no—
242C4⋊C4—104no—
243C4⋊C4—108no—
244C4⋊C4—104no—
245C4⋊C4—208no—
246C4⋊C4—208no—
247C4⋊C4—204no—
248C4⋊C4—202no—
249C4⋊C4—208no—
250C42—24no—
251C42—24no—
252C2×C5#210018yescomplemented
253C2×C5C2×#40011yescharacteristic
254C2×C5C2×#47611yescharacteristic
255C2×C5C2×#47711yescharacteristic
256C2×C5C2×#48111yescharacteristic
257C2×C5C2×#48411yescharacteristic
258C2×C5C2×#48711yescharacteristic
259C2×C5C2×#49011yescharacteristic
260C23#402112yes—
261C23#403212yes—
262C23#404312yes—
263C23C2×#67712yes—
264C23C2×Dic2012yes—
265C23#405412yes—
266C23#405412yes—
267C23C22×D2011yescharacteristic
268C2×C4—28no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—28no—
274C2×C4—104no—
275C2×C4—202no—
276C2×C4—202no—
277C2×C4—208no—
278C2×C4—204no—
279C2×C4—202no—
280C2×C4—204no—
281C2×C4—204no—
282C2×C4—202no—
283C2×C4—202no—
284C2×C4—404no—
285C2×C4—408no—
286C2×C4#402112yes—
287C2×C4#402518yes—
288C2×C4#403212yes—
289C2×C4#403518yes—
290C2×C4#404312yes—
291C2×C4C2×#67714yes—
292C2×C4C2×Dic2014yes—
293C2×C4C2×#70912yes—
294C2×C4C2×#71111yescharacteristic
295C2×C4C2×#71112yes—
296C2×C4C2×Q8×D511yescharacteristic
297C8—44no—
298C5C2×#210011yescharacteristic, complemented, Sylow
299C22#6494814yes—
300C22#6497014yes—
301C22#6500214yes—
302C22#6501114yes—
303C22#6502414yes—
304C22#6513114yes—
305C22#6513914yes—
306C22C2×#402111yescharacteristic
307C22C2×#403211yescharacteristic
308C22C2×#404311yescharacteristic
309C22C22×#67711yescharacteristic
310C22C22×Dic2011yescharacteristic
311C22C2×#405411yescharacteristic
312C22C2×#405411yescharacteristic
313C4—24no—
314C4—24no—
315C4—204no—
316C4—404no—
317C4—402no—
318C4#6494814yes—
319C4C2×#402512yes—
320C4C2×#403512yes—
321C2#1059943618yesdirect product factor
322C2C2×#6494811yescharacteristic
323C2C2×#6497011yescharacteristic
324C2C2×#6500211yescharacteristic
325C2C2×#6502411yescharacteristic
326C2C2×#6501111yescharacteristic
327C2C2×#6513111yescharacteristic
328C2C2×#6513911yescharacteristic
subgroupG/H
centerC24C2×D20
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC2×C5×#336C2
socle, prime radicalC24×C5C2×D4
hypercenterC2×#336D5
hypocenterC5C2×#2100
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. #10599436C2direct (N × H)
252. C2×C5#2100semidirect
298. C5C2×#2100semidirect
321. C2#10599436direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#652172
C2×#652242
C2×C5×#3362
C2×#647712
#105994362
C2×#21005